Given that I am strongly considering a career in academic economics, I am very much a believer in mathematical modeling. Economic interactions are really complicated, and I personally don’t have the intellectual power to even attempt to understand how the economy “really is.” Thus, if I want to develop an understanding of something, I must make simplifying assumptions. Simplifying to the point of triviality (kind of like building a model :-0 ), this is my outline of how we build a model of something in the world.

1. We assume there is a “real world out there,” and proceed to make observations.

2. We perhaps notice some regularities in how stuff happens.

3. We choose some fundamental assumptions (useful lies, one could say) which allow us to build a theory.

4. We derive the consequences of our assumptions to make predictions about how the world works.

5. We do, or tell some empiricist to do because we are lazy theorists, an experiment or look at a data set and see if our ideas cut the mustard.

From this process, we get a mathematical model (yay). A falsifiable model will spit some numbers out which are supossed to be measurable in the real world, which we can then test. The model will then enter one of two categories- possibly right (since it has not yet been falsified), or wrong. As time goes on, this process of falsification allows us to keep the level of bullshit in our models pretty low. A falsifiable model has to be right in some very general sense of the word in order not to be thrown out. However, this does not mean that a not yet falsified model describes the world as it “actually is.” For example, no sane economist would ever actually tell you that there is some time independent thing called a utility function or objective measure of happiness which your behavior necessarily maximizes. One could only say that assuming that people maximize utility allows one to make useful inferences about the world.

To me, this is the largest philosophical stumbling block in the process of mathematical modeling. I could very well model, say, continental drift by the actions of the tooth fairy and get a falsifiable model which makes good predictions. From the austere perspective of mathematical modeling, such a model is exactly as good as any other which makes the same predictions. From a positive, empirical point of view, a model reduces to simply making assumptions to make predictions. Any assumption we make must in some sense be false, as any simplification of reality is, but this does not matter. There is no metaphysics in mathematical model building! In part two, I will hope to extend this claim and thereby touch on some fundamental issues in my logical positivism.